This paper concerns two notions of rank of fuzzy matrices: maximal column rank and column rank. We investigate the difference of them. We also characterize the linear operators which preserve the maximal column rank of fuzzy matrices. That is, a linear operator T preserves maximal column rank if and only if it has the form T(X) = UXV with some invertible fuzzy matrices U and V.
Let k be a commutative field. Let G be a locally finite group without elements of order p in case char k = p > 0. In this paper it is proved that the type I∞ part of the maximal right quotient ring of the group algebra kG is zero.
Medial modes, a natural generalization of normal bands, were investigated by Płonka. Rectangular algebras, a generalization of rectangular bands (diagonal modes) were investigated by Pöschel and Reichel. In this paper we show that each medial mode embeds as a subreduct into a semimodule over a certain ring, and that a similar theorem holds for each Lallement sum of cancellative modes over a medial mode. Similar results are obtained for rectangular algebras. The paper generalizes earlier results...
Let be a ring. We recall that is called a near pseudo-valuation ring if every minimal prime ideal of is strongly prime. Let now be an automorphism of and a -derivation of . Then is said to be an almost -divided ring if every minimal prime ideal of is -divided. Let be a Noetherian ring which is also an algebra over ( is the field of rational numbers). Let be an automorphism of such that is a -ring and a -derivation of such that for all . Further, if for any...